Preheat oven to 375°F (190°C)
In a small bowl, whisk together the garam masala, smoked paprika, salt, black pepper, and olive oil.
Line a rimmed baking tray with foil and spray it with cooking spray. If you don't have cooking spray, add a few drops of oil to the foil and, using your fingers, rub it around on the foil.
Rinse the potatoes and carrots and chop them up into bite-sized pieces. Peel and chop the onion. Peel the garlic cloves.
Place the chopped veggies, whole garlic cloves, and chicken drumsticks on the foil-lined rimmed baking sheet. Now, there are two ways to add the flavored oil. One, drizzle the flavored oil all over the chicken and veggies and, using your hands, rub the mix into everything. Or, two (my preferred method), use a pastry brush or any cooking brush and brush the flavored oil onto the chicken and veggies so they are well-coated with the seasonings.
Cover the baking pan with the chicken and veggies tightly with foil and bake at 375°F (190°C). This steams the chicken to keep it juicy.
Then, the baking sheet out of the oven. Remove the foil and roast for another 20-25 minutes, until the internal temperature reaches 165°F (74°C).
Remove from the oven and let sit for about five minutes. Serve as is, or garnish it with some chopped fresh parsley or cilantro and red pepper flakes, and enjoy!